Dose reduction for x-ray CT has taken on substantial importance with the increased use of this imaging modality and the imaging of younger patients. The objective of this work is to develop and demonstrate the technical and commercial feasibility of a novel computationally-based approach to the reduction of patient xray dose in diagnostic CT scanners. The approach will use iterative algorithms for the image formation, which can produce high-quality images from low-dose data by incorporating detailed models of the physics and statistics of the data acquisition process. To date, such iterative algorithms have been little used in practice due to their high computational complexity. This problem will be solved by using revolutionary fast algorithms for the backprojection and reprojection steps in the iterative algorithm. The fast approaches to backprojection and reprojection were developed and patented by the University of Illinois. Using this technology, speed-up factors of 10x - 50x have been achieved in software demos. Accordingly, the Phase I aims of this project are to 1) Develop and implement fast statistical and physics-based iterative algorithms for reduced-dose high-precision tomography, and to 2) Evaluate and optimize performance of the fast algorithms in terms of image quality, dose reduction, and computational requirements. In Phase II, the methodology and algorithms will be extended to the dominant imaging geometries: helical multislice, conebeam with a circular source trajectory, and helical conebeam. Significant attention will be devoted to thorough testing of the new dose reduction methods. Commercial adoption of this technology by scanner manufacturers will be encouraged by the potential for increased market share owing to superior low-dose performance; increased sales of CT equipment for dose-critical applications such as pediatric, real-time, and interventional imaging; and affordability. This project promises to revolutionize CT as we know it, by making iterative algorithm-based dose reduction feasible for the first time.